Adaptively Secure Functional Encryption for Finite Languages from DLIN Assumption.
Tapas Pandit, Rana Barua · 2014
In this paper, we present Functional Encryption (FE) schemes for finite languages from standard static assumption, viz., Decisional Linear (DLIN) assumption. These finite languages are described by Deterministic Finite Automatas (DFAs). Our first scheme is ciphertext-policy functional encryption (CP-FE), where a key SKw is labeled with a string w over a fixed alphabet Σ and a ciphertext CM is associated with a DFA M over the same alphabet Σ. The key SKw can extract the message from the ciphertext CM if the DFA M accepts the string w. This CP-FE scheme is constructed based on attribute-based encryption (ABE) structure of Okamoto-Takashima in Asiacrypt, 2012. To achieve the adaptive security, we put bounds on number of occurrences of any symbol in a string and in the set of transition tuples of a DFA. Due to this restriction, the size of key space (where the keys are indexed with strings) is reduced to finite. Hence, the functional scope of any DFA in our system can capture only finite language. Similarly, we obtain our second adaptively secure FE scheme in key-policy flavor from DLIN assumption. Both the schemes are shown to be secure in the standard model. 1